MATH 115 QUIZ 5 NAME: _______________________________ May-July, 2016 Instructor: B. Stec I have completed this assignment myself, working independently and not consulting anyone except the instructor. INSTRUCTIONS The quiz is worth 100 points. There are 10 problems. This quiz is open book and open notes. This means that you may refer to your textbook, notes, and online classroom materials, but you must work independently and may not consult anyone (and confirm this with your submission). You may take as much time as you wish, provided you turn in your quiz no later than Monday, July 4. Show work/explanation where indicated. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is acceptable also. In your document, be sure to include your name and the assertion of independence of work. General quiz tips and instructions for submitting work are posted in the Quizzes module. If you have any questions, please contact me by e-mail. 1. (5 pts) The note 'G' above the note 'middle C' is a sound wave with ordinary frequency f = 392 Hertz = 392 cycles/second. State a sinusoid which models this note, assuming that the amplitude is 1 and the phase shift is 0. (no explanation required) 2. (10 pts) Solve the equation sin(2) = 2 sin() , finding all solutions in the interval [0, 2). Show work. (You should be able to provide the exact values of the solutions and state them in radians.) 3. (10 pts) Solve the equation cos() cot() + 3 cos() = 0, finding all solutions in the interval [0, 360). Show work. HINT: Start by factoring the left side of the equation, noting that cos x is a factor. (You should be able to provide the exact values of the solutions and state them in degrees.) 4. (10 pts) Solve the equation 3 arccos(2) = 2. Show work. 5. (10 pts) For the triangle ABC, we are given that C = 65, a = 16.0, and c = 24.0. (Side a is the side opposite angle A, side b is the side opposite angle B, and side c is the side opposite angle C.) Solve the triangle; that is, find the two remaining angles and the remaining side. Report angles to the nearest degree and the length rounded to one decimal place. Show work. 6. (10 pts) A real estate lot has the shape of an isosceles triangle. (Isosceles means two sides of the same length.) The lot is bounded by Maple Street, Pine Street, and Elm Street. The sides of the lot bounded by Maple and Pine are 175 feet long. Pine and Elm streets intersect at an angle of 40. Find the area of the triangular lot. One acre is 43,560 square feet. Find the area of the lot, measured in acres (to the nearest hundredth of an acre). Show work. (Sketch not to scale) 7. (10 pts) Two hikers leave the same tent at a campground and go separate ways. One hiker walks 9 miles directly south to Arkton, and the other hiker walks 15 miles directly northwest (i.e., N45W) to Benton. (Assume that the terrain is flat.) How far apart are Arkton and Benton (by the most direct route)? Show work. (You may find it very helpful to draw a picture, but you do not need to submit it.) Round your answer to the nearest tenth of a mile. 8. (10 pts) The Pentagon in Washington D.C. is 921 feet long on each of the five exterior sides. C 54 A 54 921 ft. B What is the distance from a vertex to the center of the Pentagon? That is, what is the distance between A and C? Show work. Round the distance to the nearest foot. 9. (10 pts) An airplane proceeds at a bearing of N60E, flying at 480 miles per hour. (no explanations required) (a) State the angle in standard position which corresponds to the bearing N60E. (b) Find the easterly and northerly components of the airplane's velocity. That is, find the component form of the vector which has a magnitude of 480 and makes the angle with the positive x-axis. (Use the value of you stated in part (a).) State the exact values and also give approximations to the nearest mile per hour. 10. (15 pts) Let = 3, 1 and = 2, - 4. (Work required only for parts e and f, on the next page.) (a) Which of the following graphs shows these two vectors? Choose I, II, III, or IV. (I) (II) (III) (IV) (b) Find 5 + 6 and state the result in component form. (c) State the exact magnitude (length) of and the exact magnitude of . (d) State the dot product . (e) Determine the angle between and . Show work. Write the exact angle as the arccosine of an appropriate number. Also, use a calculator to approximate the value of the angle, rounding the result to the nearest degree